A body of mass 5kg moving with a velocity of 10ms-1 collides with a stationary body of mass 6kg. If the two bodies stick together and move in the same direc...
A body of mass 5kg moving with a velocity of 10ms-1 collides with a stationary body of mass 6kg. If the two bodies stick together and move in the same direction after their collision, calculate their common velocity
Answer Details
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it. In this case, the initial momentum of the system is: pi = m1v1 + m2v2 where m1 and v1 are the mass and velocity of the first body, and m2 and v2 are the mass and velocity of the second body. Substituting the given values, we get: pi = (5 kg)(10 m/s) + (6 kg)(0 m/s) = 50 kg m/s After the collision, the two bodies stick together and move with a common velocity, which we can call vf. Using the law of conservation of momentum again, we can write: pf = (m1 + m2)vf where pf is the final momentum of the system. Since no external forces act on the system, the initial and final momenta must be equal: pi = pf Substituting the values we obtained earlier and solving for vf, we get: 50 kg m/s = (5 kg + 6 kg)vf vf = 4.55 m/s Therefore, the common velocity of the two bodies after the collision is 4.55 m/s. Answer is correct.